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Mirrors > Home > ILE Home > Th. List > riotaprop | Unicode version |
Description: Properties of a restricted definite description operator. Todo (df-riota 5738 update): can some uses of riota2f 5759 be shortened with this? (Contributed by NM, 23-Nov-2013.) |
Ref | Expression |
---|---|
riotaprop.0 |
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riotaprop.1 |
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riotaprop.2 |
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Ref | Expression |
---|---|
riotaprop |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | riotaprop.1 |
. . 3
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2 | riotacl 5752 |
. . 3
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3 | 1, 2 | eqeltrid 2227 |
. 2
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4 | 1 | eqcomi 2144 |
. . . 4
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5 | nfriota1 5745 |
. . . . . 6
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6 | 1, 5 | nfcxfr 2279 |
. . . . 5
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7 | riotaprop.0 |
. . . . 5
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8 | riotaprop.2 |
. . . . 5
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9 | 6, 7, 8 | riota2f 5759 |
. . . 4
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10 | 4, 9 | mpbiri 167 |
. . 3
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11 | 3, 10 | mpancom 419 |
. 2
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12 | 3, 11 | jca 304 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1335 df-nf 1438 df-sb 1737 df-eu 2003 df-clab 2127 df-cleq 2133 df-clel 2136 df-nfc 2271 df-rex 2423 df-reu 2424 df-rab 2426 df-v 2691 df-sbc 2914 df-un 3080 df-in 3082 df-ss 3089 df-sn 3538 df-pr 3539 df-uni 3745 df-iota 5096 df-riota 5738 |
This theorem is referenced by: lble 8729 |
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